<script id="draw-shader-vs" type="x-shader/x-vertex">
precision mediump float;

attribute vec3 inPos;
attribute vec3 inNV;
attribute vec3 inCol;

varying vec3 vertPos;
varying vec3 vertNV;
varying vec3 vertCol;

uniform mat4  u_projectionMat44;
uniform mat4  u_viewMat44;
uniform mat4  u_modelMat44;
uniform vec2  u_depthRange;
uniform float u_projection;

const float cPi = 3.141593;

void main()
{
    vec3 modelNV  = mat3( u_modelMat44 ) * normalize( inNV );
    vertNV        = mat3( u_viewMat44 ) * modelNV;
    vertCol       = inCol;
    vec4 modelPos = u_modelMat44 * vec4( inPos, 1.0 );
    vec4 viewPos  = u_viewMat44 * modelPos;
    vertPos       = viewPos.xyz / viewPos.w;
    
    vec2 dirXY    = normalize( vec2( -viewPos.z, viewPos.x ) );
    vec2 dirZ     = normalize( vec2( length(viewPos.xz), viewPos.y ) );
    float posX    = asin( abs( dirXY.y ) ) * 2.0 / cPi;
    float posY    = asin( abs( dirZ.y ) ) * 2.0 / cPi;
    vec3 prjPos = vec3(
        0.5 * sign( dirXY.y ) * mix(2.0-posX, posX, step(0.0, dirXY.x) ),
        sign( dirZ.y ) * posY,
        2.0 * (length(viewPos.xyz)-u_depthRange.x) / (u_depthRange.y-u_depthRange.x) - 1.0 );
    gl_Position   = mix( vec4( prjPos.xyz, 1.0 ), u_projectionMat44 * viewPos, u_projection );
}
</script>

<script id="draw-shader-fs" type="x-shader/x-fragment">
precision mediump float;

varying vec3 vertPos;
varying vec3 vertNV;
varying vec3 vertCol;

uniform vec3  u_lightDir;
uniform float u_ambient;
uniform float u_diffuse;
uniform float u_specular;
uniform float u_shininess;

void main()
{
    vec3 color      = vertCol;
    vec3 lightCol   = u_ambient * color;
    vec3  normalV   = normalize( vertNV );
    vec3  lightV    = normalize( -u_lightDir );
    float NdotL     = max( 0.0, dot( normalV, lightV ) );
    lightCol       += NdotL * u_diffuse * color;
    vec3  eyeV      = normalize( -vertPos );
    vec3  halfV     = normalize( eyeV + lightV );
    float NdotH     = max( 0.0, dot( normalV, halfV ) );
    float kSpecular = ( u_shininess + 2.0 ) * pow( NdotH, u_shininess ) / ( 2.0 * 3.14159265 );
    lightCol       += kSpecular * u_specular * color;
    gl_FragColor    = vec4( lightCol.rgb, 1.0 );
}
</script>

<style>
html,body { margin: 0; overflow: hidden; }
#gui { position : absolute; top : 0; left : 0; font-size : large; }
#ref-link { position : absolute; bottom : 0; left : 0; font-size : large; }  
</style>

<body onload>

<form id="gui" name="inputs">
<table>
    <tr> <td> <font color= #CCF>projection</font> </td> <td>
        <select id="projection">>
            <option value="0">spherical</option>
            <option value="1">perspectiv</option>
        </select>
    </td> </tr>
</table>
</form>

<canvas id="projection-canvas" style="border: none;" width="100%" height="100%"></canvas>

<a id="ref-link" href="https://stackoverflow.com/questions/46151527/projection-matrix-for-pseudo-cylindrical-projection/46162819#46162819">
<font color= #CCF>Projection Matrix for Pseudo Cylindrical Projection</font> 
</a>

</body>

<script type="text/javascript">

(function loadscene() {

var sliderScale = 100.0
var gl, canvas, vp_size, progDraw, bufCube = {}, bufTorus = {};

function render(deltaMS){

    var projection = document.getElementById( "projection" ).value;

    Camera.create();
    Camera.vp = [canvas.width, canvas.height];
    var currentTime = Date.now();   
        
    gl.viewport( 0, 0, canvas.width, canvas.height );
    gl.enable( gl.DEPTH_TEST );
    gl.clearColor( 0.0, 0.0, 0.0, 1.0 );
    gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );
    gl.enable( gl.CULL_FACE );
    gl.cullFace( gl.BACK );
    gl.frontFace( gl.CCW );

    // set up draw shader
    ShProg.Use( progDraw );
    ShProg.SetM44( progDraw, "u_projectionMat44", Camera.Perspective() );
    ShProg.SetM44( progDraw, "u_viewMat44", Camera.LookAt() );
    ShProg.SetF2( progDraw, "u_depthRange", [ Camera.near, Camera.far ] );
    ShProg.SetF1( progDraw, "u_projection", projection )
    ShProg.SetF3( progDraw, "u_lightDir", [-1.0, -0.5, -2.0] );
    ShProg.SetF1( progDraw, "u_ambient", 0.2 );
    ShProg.SetF1( progDraw, "u_diffuse", 0.7 );
    ShProg.SetF1( progDraw, "u_specular", 0.8 );
    ShProg.SetF1( progDraw, "u_shininess", 10.0 );
    var modelMat = IdentM44()
    modelMat = RotateAxis( modelMat, CalcAng( deltaMS, 10.0 ), 2 );
    modelMat = Translate( modelMat, [0.0, -2.5, 0.0] );
    modelMat = RotateAxis( modelMat, CalcAng( deltaMS, 13.0 ), 0 );
    modelMat = RotateAxis( modelMat, CalcAng( deltaMS, 17.0 ), 1 );
    ShProg.SetM44( progDraw, "u_modelMat44", modelMat );

    // draw scene
    VertexBuffer.Draw( bufTorus );

    requestAnimationFrame(render);
}

function initScene() {

    document.getElementById( "projection" ).value = 0;
    
    canvas = document.getElementById( "projection-canvas");
    vp_size = [canvas.width, canvas.height];
    gl = canvas.getContext( "experimental-webgl" );
    if ( !gl )
      return;

    progDraw = ShProg.Create( 
      [ { source : "draw-shader-vs", stage : gl.VERTEX_SHADER },
        { source : "draw-shader-fs", stage : gl.FRAGMENT_SHADER }
      ] );
    progDraw.inPos = gl.getAttribLocation( progDraw.progObj, "inPos" );
    progDraw.inNV  = gl.getAttribLocation( progDraw.progObj, "inNV" );
    progDraw.inCol = gl.getAttribLocation( progDraw.progObj, "inCol" );
    if ( progDraw.progObj == 0 )
        return;

    // create torus
    var circum_size = 32, tube_size = 32;
    var rad_circum = 1.0;
    var rad_tube = 0.5;
    var torus_pts = [];
    var torus_nv = [];
    var torus_col = [];
    var torus_inx = [];
    var col = [1, 0.5, 0.0];
    for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
        var center = [
            Math.cos(2 * Math.PI * i_c / circum_size),
            Math.sin(2 * Math.PI * i_c / circum_size) ]
        for ( var i_t = 0; i_t < tube_size; ++ i_t ) {
            var tubeX = Math.cos(2 * Math.PI * i_t / tube_size)
            var tubeY = Math.sin(2 * Math.PI * i_t / tube_size)
            var pt = [
                center[0] * ( rad_circum + tubeX * rad_tube ),
                center[1] * ( rad_circum + tubeX * rad_tube ),
                tubeY * rad_tube ]
            var nv = [ pt[0] - center[0] * rad_tube, pt[1] - center[1] * rad_tube, tubeY * rad_tube ]
            torus_pts.push( pt[0], pt[1], pt[2] );
            torus_nv.push( nv[0], nv[1], nv[2] );
            torus_col.push( col[0], col[1], col[2] );
            var i_cn = (i_c+1) % circum_size
            var i_tn = (i_t+1) % tube_size
            var i_c0 = i_c * tube_size; 
            var i_c1 = i_cn * tube_size; 
            torus_inx.push( i_c0+i_tn, i_c0+i_t, i_c1+i_t, i_c0+i_tn, i_c1+i_t, i_c1+i_tn )
        }
    }
    bufTorus = VertexBuffer.Create(
      [ { data : torus_pts, attrSize : 3, attrLoc : progDraw.inPos },
        { data : torus_nv,  attrSize : 3, attrLoc : progDraw.inNV },
        { data : torus_col, attrSize : 3, attrLoc : progDraw.inCol } ],
        torus_inx
    );

    window.onresize = resize;
    resize();
    requestAnimationFrame(render);
}

function resize() {
    //vp_size = [gl.drawingBufferWidth, gl.drawingBufferHeight];
    vp_size = [window.innerWidth, window.innerHeight];
    //vp_size = [512, 256];
    canvas.width = vp_size[0];
    canvas.height = vp_size[1];
}

glArrayType = typeof Float32Array !="undefined" ? Float32Array : ( typeof WebGLFloatArray != "undefined" ? WebGLFloatArray : Array );

function IdentM44() {
  var m = new glArrayType(16);
  m[0]  = 1; m[1]  = 0; m[2]  = 0; m[3]  = 0;
  m[4]  = 0; m[5]  = 1; m[6]  = 0; m[7]  = 0;
  m[8]  = 0; m[9]  = 0; m[10] = 1; m[11] = 0;
  m[12] = 0; m[13] = 0; m[14] = 0; m[15] = 1;
  return m;
};

function RotateAxis(matA, angRad, axis) {
    var aMap = [ [1, 2], [2, 0], [0, 1] ];
    var a0 = aMap[axis][0], a1 = aMap[axis][1]; 
    var sinAng = Math.sin(angRad), cosAng = Math.cos(angRad);
    var matB = new glArrayType(16);
    for ( var i = 0; i < 16; ++ i ) matB[i] = matA[i];
    for ( var i = 0; i < 3; ++ i ) {
        matB[a0*4+i] = matA[a0*4+i] * cosAng + matA[a1*4+i] * sinAng;
        matB[a1*4+i] = matA[a0*4+i] * -sinAng + matA[a1*4+i] * cosAng;
    }
    return matB;
}

function Translate( matA, trans ) {
    var matB = new glArrayType(16);
    for ( var i = 0; i < 16; ++ i ) matB[i] = matA[i];
    for ( var i = 0; i < 3; ++ i )
        matB[12+i] = matA[i] * trans[0] + matA[4+i] * trans[1] + matA[8+i] * trans[2] + matA[12+i];
    return matB;
}

function Cross( a, b ) { return [ a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0], 0.0 ]; }
function Dot( a, b ) { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; }
function Normalize( v ) {
    var len = Math.sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
    return [ v[0] / len, v[1] / len, v[2] / len ];
}

var Camera = {};
Camera.create = function() {
    this.pos    = [0, 0, 0.0];
    this.target = [0, -1, 0];
    this.up     = [0, 0, 1];
    this.fov_y  = 120;
    this.vp     = [800, 600];
    this.near   = 0.5;
    this.far    = 100.0;
}
Camera.Perspective = function() {
    var fn = this.far + this.near;
    var f_n = this.far - this.near;
    var r = this.vp[0] / this.vp[1];
    var t = 1 / Math.tan( Math.PI * this.fov_y / 360 );
    var m = IdentM44();
    m[0]  = t/r; m[1]  = 0; m[2]  =  0;                              m[3]  = 0;
    m[4]  = 0;   m[5]  = t; m[6]  =  0;                              m[7]  = 0;
    m[8]  = 0;   m[9]  = 0; m[10] = -fn / f_n;                       m[11] = -1;
    m[12] = 0;   m[13] = 0; m[14] = -2 * this.far * this.near / f_n; m[15] =  0;
    return m;
}
Camera.LookAt = function() {
    var mz = Normalize( [ this.pos[0]-this.target[0], this.pos[1]-this.target[1], this.pos[2]-this.target[2] ] );
    var mx = Normalize( Cross( this.up, mz ) );
    var my = Normalize( Cross( mz, mx ) );
    var tx = Dot( mx, this.pos );
    var ty = Dot( my, this.pos );
    var tz = Dot( [-mz[0], -mz[1], -mz[2]], this.pos ); 
    var m = IdentM44();
    m[0]  = mx[0]; m[1]  = my[0]; m[2]  = mz[0]; m[3]  = 0;
    m[4]  = mx[1]; m[5]  = my[1]; m[6]  = mz[1]; m[7]  = 0;
    m[8]  = mx[2]; m[9]  = my[2]; m[10] = mz[2]; m[11] = 0;
    m[12] = tx;    m[13] = ty;    m[14] = tz;    m[15] = 1; 
    return m;
} 

var ShProg = {
Create: function (shaderList) {
    var shaderObjs = [];
    for (var i_sh = 0; i_sh < shaderList.length; ++i_sh) {
        var shderObj = this.Compile(shaderList[i_sh].source, shaderList[i_sh].stage);
        if (shderObj) shaderObjs.push(shderObj);
    }
    var prog = {}
    prog.progObj = this.Link(shaderObjs)
    if (prog.progObj) {
        prog.attrInx = {};
        var noOfAttributes = gl.getProgramParameter(prog.progObj, gl.ACTIVE_ATTRIBUTES);
        for (var i_n = 0; i_n < noOfAttributes; ++i_n) {
            var name = gl.getActiveAttrib(prog.progObj, i_n).name;
            prog.attrInx[name] = gl.getAttribLocation(prog.progObj, name);
        }
        prog.uniLoc = {};
        var noOfUniforms = gl.getProgramParameter(prog.progObj, gl.ACTIVE_UNIFORMS);
        for (var i_n = 0; i_n < noOfUniforms; ++i_n) {
            var name = gl.getActiveUniform(prog.progObj, i_n).name;
            prog.uniLoc[name] = gl.getUniformLocation(prog.progObj, name);
        }
    }
    return prog;
},
AttrI: function (prog, name) { return prog.attrInx[name]; },
UniformL: function (prog, name) { return prog.uniLoc[name]; },
Use: function (prog) { gl.useProgram(prog.progObj); },
SetI1: function (prog, name, val) { if (prog.uniLoc[name]) gl.uniform1i(prog.uniLoc[name], val); },
SetF1: function (prog, name, val) { if (prog.uniLoc[name]) gl.uniform1f(prog.uniLoc[name], val); },
SetF2: function (prog, name, arr) { if (prog.uniLoc[name]) gl.uniform2fv(prog.uniLoc[name], arr); },
SetF3: function (prog, name, arr) { if (prog.uniLoc[name]) gl.uniform3fv(prog.uniLoc[name], arr); },
SetF4: function (prog, name, arr) { if (prog.uniLoc[name]) gl.uniform4fv(prog.uniLoc[name], arr); },
SetM33: function (prog, name, mat) { if (prog.uniLoc[name]) gl.uniformMatrix3fv(prog.uniLoc[name], false, mat); },
SetM44: function (prog, name, mat) { if (prog.uniLoc[name]) gl.uniformMatrix4fv(prog.uniLoc[name], false, mat); },
Compile: function (source, shaderStage) {
    var shaderScript = document.getElementById(source);
    if (shaderScript)
        source = shaderScript.text;
    var shaderObj = gl.createShader(shaderStage);
    gl.shaderSource(shaderObj, source);
    gl.compileShader(shaderObj);
    var status = gl.getShaderParameter(shaderObj, gl.COMPILE_STATUS);
    if (!status) alert(gl.getShaderInfoLog(shaderObj));
    return status ? shaderObj : null;
},
Link: function (shaderObjs) {
    var prog = gl.createProgram();
    for (var i_sh = 0; i_sh < shaderObjs.length; ++i_sh)
        gl.attachShader(prog, shaderObjs[i_sh]);
    gl.linkProgram(prog);
    status = gl.getProgramParameter(prog, gl.LINK_STATUS);
    if ( !status ) alert(gl.getProgramInfoLog(prog));
    return status ? prog : null;
} };

var VertexBuffer = {
Create: function(attribs, indices, type) {
    var buffer = { buf: [], attr: [], inx: gl.createBuffer(), inxLen: indices.length, primitive_type: type ? type : gl.TRIANGLES };
    for (var i=0; i<attribs.length; ++i) {
        buffer.buf.push(gl.createBuffer());
        buffer.attr.push({ size : attribs[i].attrSize, loc : attribs[i].attrLoc, no_of: attribs[i].data.length/attribs[i].attrSize });
        gl.bindBuffer(gl.ARRAY_BUFFER, buffer.buf[i]);
        gl.bufferData(gl.ARRAY_BUFFER, new Float32Array( attribs[i].data ), gl.STATIC_DRAW);
    }
    gl.bindBuffer(gl.ARRAY_BUFFER, null);
    if ( buffer.inxLen > 0 ) {
        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, buffer.inx);
        gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array( indices ), gl.STATIC_DRAW);
        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, null);
    }
    return buffer;
},
Draw: function(bufObj) {
    for (var i=0; i<bufObj.buf.length; ++i) {
        gl.bindBuffer(gl.ARRAY_BUFFER, bufObj.buf[i]);
        gl.vertexAttribPointer(bufObj.attr[i].loc, bufObj.attr[i].size, gl.FLOAT, false, 0, 0);
        gl.enableVertexAttribArray( bufObj.attr[i].loc);
    }
    if ( bufObj.inxLen > 0 ) {
        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, bufObj.inx);
        gl.drawElements(bufObj.primitive_type, bufObj.inxLen, gl.UNSIGNED_SHORT, 0);
        gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, null );
    }
    else
        gl.drawArrays(bufObj.primitive_type, 0, bufObj.attr[0].no_of );
    for (var i=0; i<bufObj.buf.length; ++i)
        gl.disableVertexAttribArray(bufObj.attr[i].loc);
    gl.bindBuffer( gl.ARRAY_BUFFER, null );
} };

function Fract( val ) { 
    return val - Math.trunc( val );
}
function CalcAng( deltaMS, interval ) {
    return Fract( deltaMS / (1000*interval) ) * 2.0 * Math.PI;
}
function CalcMove( deltaMS, intervall, range ) {
    var pos = self.Fract( deltaMS / (1000*interval) ) * 2.0
    var pos = pos < 1.0 ? pos : (2.0-pos)
    return range[0] + (range[1] - range[0]) * pos;
}    
function EllipticalPosition( a, b, angRag ) {
    var a_b = a * a - b * b
    var ea = (a_b <= 0) ? 0 : Math.sqrt( a_b );
    var eb = (a_b >= 0) ? 0 : Math.sqrt( -a_b );
    return [ a * Math.sin( angRag ) - ea, b * Math.cos( angRag ) - eb, 0 ];
}

initScene();

})();
</script>
